On Control and Optimization

The primary goal of this thesis is to study transmission line reactance tweaking, as a mechanism for both post-disturbance control and pre-disturbance resilience enhancement in a transmission network, and develop an optimization framework for evaluating the efficacy of this mechanism in both scenarios. We start by developing a mixed-integer linear programming (MILP) formulation for tracking the redistribution of direct current (DC) flows and the graph-theoretic evolution of network topology over the course of cascading failures. Next, we propose a min-max setup for studying the impact of post-disturbance reactance tweaking on the resilience of the system to a worst-case N-k disturbance and devise a MILP reformulation scheme for the underlying bilevel nonconvex mixed-integer nonlinear program (MINLP) to facilitate the computation of its optimal solution. We then develop a MILP framework for computing the exact value of a tight upper bound on the efficacy of post-disturbance reactance tweaking among the set of all possible Nk disturbances for a given k and a given bus load scenario. Our numerical case study suggests that post-disturbance reactance tweaking, even on only a small number of lines, can considerably reduce the amount of load shed in some scenarios in the tested system. As for pre-disturbance resilience enhancement, we develop a MILP reformulation for approximating the bilevel MINLP that seeks to assess the efficacy of pre-disturbance reactance tweaking in reducing the number of lines that will fail over the propagation of cascading failures in the event of a worst-case-scenario N-k disturbance. We also give a MILP framework for computing an approximate upper bound on the efficacy of this mechanism among the set of all N-k contingencies for a given k. Our numerical case study suggests that pre-disturbance reactance tweaking on a few transmission lines can, in some cases, prevent the failure of multiple transmission lines over the course of cascading failures in the tested system.